The total amount of the drink is 2L. Strawberry concentrate will be X amount, and lemon concentrate will be the other part which is 2 - X.
---Note that we can only use one variable because there is only one equation to be set up here. That's why "the other part" is simply the total amount minus the strawberry amount.
0.4(2) = 0.3(x) + 0.55(2 - x)
---0.4, 0.3 and 0.55 are the decimal equivalents of 40%, 30% and 55%
0.8 = 0.3x + 1.1 - 0.55x
0.8 = -0.25x + 1.1
-0.3 = -0.25x
x = 1.2
Therefore, Chris should use 1.2L of strawberry concentrate and 0.8L of lemon concentrate to get 2L of a 40% concentrate mixture.
Hope this helps!
a survey of 504 citizens found that 378 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? (Round to 3 decimal digits)
The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
What is a confidence interval?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We have:
A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
Sample proportion = p = 378/504 = 0.75
q = 1 - p = 1 - 0.75 = 0.25
[tex]\rm SD = \sqrt{\dfrac{pq}{n}}[/tex]
[tex]\rm SD = \sqrt{\dfrac{0.75\times0.25}{504}}[/tex]
SD = 0.01928
For 95% confidence interval Z value = 1.96
Lower limit = 0.75 - 1.96(0.01928)
= 0.712
Thus, the lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
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Consider a banking system where the Federal Reserve uses required reserves to control the money supply. (This was the case in the U.S. prior to 2008.) Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is demand deposits. To simplify the analysis, suppose the banking system has total reserves of $400. Determine the money multiplier and the money supply for each reserve requirement listed in the following table.
The determination of the money multiplier and the money supply for each reserve requirement listed in the following table are as follows:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 $8,000
10 10 $4,000
What is the money multiplier?The money multiplier is the ratio of the reserve to the money supply.
The formula for determining the money multiplier is 1/r where r is the reserve ratio.
What is the money supply?The money supply is the total amount of money circulating in the commercial banking system.
The quantity of the money supply is determined by multiplying the money multiplier by the total reserves.
Data and Calculations:Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 (1/0.05) $8,000 ($400 x 20)
10 10 (1/0.1) $4,000 ($400 x 10)
Question Completion:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5
10
Thus, the money multiplier and money supply for the 5% reserve requirement are higher than for the 10% reserve requirement.
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Let [] denote the operation a [] b = a+b - [tex]\frac{ab}{2}[/tex] ....
The only statement that holds for the given operation is Statement II
Operations and numbersGiven the following operartions
a [] b = a+b - ab/2
We need to check the true statement
For the expression x [] (y+z) = x [] y + x [] z
x [] (y+z) = x+y+z - x(y+z)/2
x [] (y+z) = x+y+z - (xy+xz)/2
x [] y +x [] z = x+y - xy/2 +[x+z - xz/2 ]
x [] y +x [] z = x+y+x+z -xy/2 - xz/2
x [] y +x [] z = 2x+y+z - (xy+xz)/2
This shows that the statement I is incorrect
For the second statement
y [] z = y+z - yz/2
x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2
x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4
For the other expression
x [] y = x+y - xy/2
(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2
(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4
This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)
For the third statement
x [] z = x+z - xz/2
y [] z = y+z - yz/2
z [] 0 = z+0 - z(0)/2
z [] 0 = z
x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z
x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2
For the expression (x+y)[] z
(x+y)[] z = (x+y)+z - (xyz)/2
Hence the statement III is not valid
Based on the explanations above, the only statement that holds for the given operation is Statement II
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If m∠B = 14°, and m∠D = 49°, what is m∠BEA?
Answer:
117 degrees
Step-by-step explanation:
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
two to the seven eighths power, all over two to the one fourth power
The expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
What are Exponents?Exponents are the base raised to a power, It is written in the superscript of a number.
The expression given in the statement can be written as
[tex]\rm \dfrac{ 2^{7/8}}{2^{1/4}}[/tex]
By the Exponent rule,
[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]
So the expression can be written as
=[tex]\rm { 2^{7/8-1/4}[/tex]=[tex]\rm 2^{5/8}[/tex]
=[tex]\rm \sqrt[8]{2^5}[/tex]
Therefore, in radical form, the expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
The complete question is
Rewrite the rational exponent as a radical by extending the properties of integer exponents.
2 to the 7 over 8 power, all over 2 to the 1 over 4 power
the eighth root of 2 to the fifth power
the fifth root of 2 to the eighth power
the square root of 2 to the 5 over 8 power
the fourth root of 2 to the sixth power
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Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire. O14 ft 15 ft 20 ft 29 ft Jason planted and staked a tree . The stakes are 21 ft from the base of the tree . They are connected to wires that attach to the trunk at a height of 20 ft . Find the length of a wire . O14 ft 15 ft 20 ft 29 ft
Answer:
29 ft
Step-by-step explanation:
The distance along the ground from one stake to the tree, 21 ft, and the distance up the trunk from the ground, 20 ft, are the legs of a right triangle. The length of the wire is the hypotenuse of the right triangle. We can use the Pythagorean theorem to solve this problem.
a² + b² = c²
(21 ft)² + (20 ft)² = c²
c² = 841 ft²
c = √(841 ft²)
c = 29 ft
Answer: 29 ft
sin A - sin B - sin C=-4cos A 2 .sin B 2 .sin C 2
sinA+sinB+sinC
=2sin(A+B)/2cos(A-B)/2+sin C
=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2
=2cosC/2(cos(A-B)/2+cos(A+B)/2)
=4 cos A/2 cos B/2 cos C/2
= RHS
The following are the temperatures in
°C for the first 12 days of January:
-5.5, 6, -1.5, 3, 4, -2.5,
0, 6.5, -3, 2.5, -1, 5.5
What is the median temperature for
those 12 days?
Give your answer as a decimal.
ABC Check
↑
XI
Answer:
1.25 is the median for the first 12 days in January
PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
The Csc θ = [tex]\frac{8}{5}[/tex] is equivalent to which of the following expressions?
A. sin θ = [tex]\frac{5}{8}[/tex]
B. cos θ = [tex]\frac{5}{8}[/tex]
C. tan θ = [tex]\frac{5}{8}[/tex]
D. sin θ = [tex]\frac{8}{5}[/tex]
E. cos θ = [tex]\frac{8}{5}[/tex]
F. tan θ = [tex]\frac{8}{5}[/tex]
Answer:
A. sin θ = 5/8
Step-by-step explanation:
csc θ = 1/sin θ
csc θ = 8/5
1/sin θ = 8/5
sin θ = 5/8
Robert has 3/4 of a candy bar like he wants to share it with himself and two friends what fraction of the candy bar will each person get?
Answer:
significa que 1 barra de chocolate dividida entre 4 amigos es igual a 1 4. Por lo tanto, cada persona recibe 1 4 de la barra”. 6.
Step-by-step explanation:
Answer:
3/4 divided by 3 is 0.25
Step-by-step explanation:
We know that he has 3/4 of a candy bar and he wants to share it with himself plus 2 people.
The expression 3/4 divided by 3 represents this.
To change division to multiplication we use the reciprocal.
3/4 times 1/3 is 0.25.
Hope this helps. (:
Kristina invests a total of $28,500 in two accounts. The first account earned a rate of return of 10% (after a year). However, the second account suffered a 4% loss in the same time period. At the end of one year, the total amount of money gained was $1,310.00. How much was invested into each account?
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 10% and y represent the amount of money invested at a loss of 4%, hence:
x + y = 28500 (1)
Also:
(x * 1 year * 0.1) + (y * 1 year * -0.04) = 1310
0.1x - 0.04y = 1310 (2)
From equation 1 and 2:
x = 17500, y = 11000
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
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A runner can run 3miles in 15 minutes. At this rate, how many miles can he run in 45minutes?
Answer:
9 miles
Step-by-step explanation:
If 3 miles is equal to 15 mins
Then you do 3 miles and times by 3 cause if you times 15 by 3, you'll get 45 mins
So the answer= 9 miles
vase with a circular base exerts a force of 15 N on a table with a pressure of 700 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
radius =
cm
The radius of the base is 8.245 cm
Given, a vase with a circular base exerts
Pressure = 700 N/m²
Force = 15 N
Area = ?
∴ area = πr²
By finding out the area of the vase we can calculate the radius.
We know that Pressure = Force/Area
According to the equation, pressure is inversely related to area but directly related to force. Pressure rises at a constant area as the force exerted increases in strength.
therefore apply the above the formula to find out the area and radius.
700 = 15/πr²
πr² = 15/700
πr² = 3/140
r² = 3/140 × 3.14
since π value is 3.14
r² = 0.0068
r = √0.0068
r = 0.0824 m
r = 0.0824 × 100
r = 8.245 cm
we get radius as 8.245 .
Hence we get the radius of the base of the vase as 8.245 cm.
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Determine the equation of the linear function that generates the following table of values.
Answer:
y = -19x + 14
Step-by-step explanation:
For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14
z varies directly as x^3 and inversely as y^3. if z=59 when x=8 and y=8, find Z if x=3 and y=4
[tex]z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}[/tex]
Question 6 of 10
If and
A.D
BD B.C
are rational expressions, then:
OA. True
OB. False
The expression a/b ÷ c/d = ad/bc is A. true.
Given to show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc.
The ratio of two polynomials is an example of a rational expression. If an expression f is rational, it can be expressed in the form p/q, where p and q are polynomials.
Here we have a ,b ,c and d in the form of p/q form.
We take the reciprocal of the expression on the right side of the division sign when the rational expression a/b is to be divided by the rational expression c/d.
so, L.H.S = a/b ÷ c/d
= a/b × 1/(c/d)
= a/b × d/c
= ad/bc
= R.H.S
since L.H.S = R.H.S
a/b ÷c/d = ad/bc
Hence the expression a/b ÷ c/d = ad/bc is A.true.
Your question was incomplete. Please find the missing content here.
If A/B and C/D are rational expressions, then: A/B ÷C/D
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-2+12-2^3 divided by 2^0 times 3
Answer:
The correct answer is -14
Step-by-step explanation:
Prove: m∠TSE + m∠RSO = m∠TSK
Answer:
down there
Step-by-step explanation:
we can see that angel rso and esk are congruent because they are verticle angels.
we also know that angel tse plus esk is equal to tsk, so angel tse+rso=tsk by algebra
Does anyone how to solve this sum? It’s urgent
The required value for the sum is 9580.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
Simplification in mathematics to solve the given condition on its operators.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
= [tex]\frac{10000}{1.028^2} +68*\frac{1-\frac{1}{1.028^2} }{\frac{0.115}{4} } \\9451+68*\frac{1-0.94}{\frac{0.115}{4} } \\\\9451+68*\frac{0.054}{\frac{0.115}{4} } \\\\\\9451+3.72{\frac{4}{0.115} } \\\\\\9451+129\\[/tex]
= 9580
The required solution is given as 9580.
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The lines shown below are perpendicular.
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
The lines shown below are perpendicular. Is this statement true or false?
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
In order for a pair of lines to be perpendicular, they must intersect at a [tex]\bf{90^\circ}[/tex] angle. (a right angle)
[tex]\bf{Since\;the\;green\;line\;and\;the\;red\;one\;intersect\;at\;a\;right\;angle,}\\they\;are\;perpendicular.\\\\Hope\;you\;will\;have\;a\;fantabulous\;day!}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
If there are 3 liquids in a Density column, which liquid would be the least dense?
The liquid on the bottom of the column.
The liquid floating on the top.
The liquid in between the liquid on the top of the column and the liquid on the bottom layer of the column.
The liquid that will be the least dense liquid in the density column is; The liquid floating on the top.
How to identify least dense liquid?
The formula for density is;
Density = Mass/Volume
Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.
Thus, this means that the liquid that is most dense will be at the bottom of the liquid.
The liquid that is least dense will be at the top of the liquid.
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Find the following sums ( for letter C)
Each number in the sum is even, so we can remove a factor of 2.
2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)
Use whatever technique you used in (a) and (b) to compute the sum
1 + 2 + 3 + 4 + ... + 39 + 40
With Gauss's method, for instance, we have
S = 1 + 2 + 3 + ... + 38 + 39 + 40
S = 40 + 39 + 38 + ... + 3 + 2 + 1
2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41
S = 20×21 = 420
Then the sum you want is 2×420 = 840.
What is the value of the following radical expression?
Answer:
b.) 2
Explanation:
Given:
[tex]\sf - \sqrt[\sf 5]{\sf -32}[/tex]rewrite knowing 2⁵ = 32, (-2)⁵ = -32
[tex]\sf -\left(\sqrt[5]{(-2)^5}\right)[/tex]simplify, ⁿ√xⁿ = x
[tex]\sf -\left(-2}\right)[/tex]distribute inside parenthesis
[tex]\sf 2[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$}[/tex]
{ Pisces04 }6x^2+18x=0 rounded the nearest 10th
By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.
How to solve a quadratic equation
In this question we must apply algebraic rules to find the roots of a quadratic equation, the roots are the values of the equation such that is equal to zero. Now we present the complete procedure:
6 · x² + 18 · x = 0
6 · x · (x + 3) = 0
x = 0 ∨ x = - 3
By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.
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What is the domain of the following relation?
{(-3, -8), (-2, 9), (1, -1), (5,3)}
O {-8, -1, 3, 9}
O {-3, -2, 1, 5}
O (-3, -8)
O {-8, -3, -2, -1, 1, 3, 5, 9}
Answer: {-3, -2, 1, 5}
Step-by-step explanation:
The domain is the set of x-values.
Which of the following is a true statement
5/6 > 10/12
8/16=1/4
3/4<4/6
11/15<4/5
Answer:
11/15 < 4/5
Step-by-step explanation:
1. 5/6 = 10/12, so the first answer is not correct
2. 1/4 = 4/16, so the second answer is not correct
3. 3/4 = 9/12 and 4/6 = 8/12, so the third answer is not correct
4. 4/5 = 12/15 > 11/15, so this answer is correct
A shirt and a tie together cost $57. The shirt costs $33 more than the tie. What is the cost of the shirt?
Answer:
Shirt: $45 , Tie: $12
Step-by-step explanation:
Let s be the price of the shirt
Let t be the price of the tie
Given the information from the question,
s + t = 57 - Equation 1
s - t = 33 - Equation 2
We will use substitution method to find the prices.
We will rearranging equation 1.
s = 57 - t
We will substitute s into equation 2.
57 - t - t = 33
57 - 2t = 33
-2t = 33 - 57
-2t = -24
t = -24 / -2
= 12
We now substitute t into Equation 1.
s + 12 = 57
s = 57 - 12
= 45
From here we know, the shirt costs $45 and the tie costs $12
A video game randomly chooses your car color and type. The
probability of getting a red car is 0.20, and the probability of
a getting a convertible is 0.30.
Event A = You get a red car.
Event B = You get a convertible.
A and B are independent events if
• A. The probability of getting a red car or a convertible is 0.06.
O
B. The probability of getting a red convertible is 0.06.
• C. The probability of getting a red car or a convertible is 0.50.
O D. The probability of getting a red convertible is 0.
The correct statement regarding when the events will be independent is given as follows:
B. The probability of getting a red convertible is 0.06.
What are independent events?Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem, the probabilities are given as follows:
P(A) = 0.2.P(B) = 0.3.The events will be independent if:
[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]
The intersection of events A and B is a red convertible car, hence the correct option is:
B. The probability of getting a red convertible is 0.06.
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Find the range of the parent function below. y = |x| A. all real numbers B. all positive numbers C. all positive numbers and 0 D. all negative numbers
Answer:
c
Step-by-step explanation:
absolute values are positive and abs value of 0 = 0
n August 31 of the current year, the assets and liabilities of Gladstone, Inc. are as follows: Cash $27,900; Supplies, $900; Equipment, $8,500; Accounts Payable, $7,300. What is the amount of stockholders’ equity as of August 31 of the current year?
The amount of stockholders’ equity as of August 31 of the current year is $26400.
How to calculate the equity?The owner's equity will be:
= Cash + Supplies + Equipment - Account payable
= 27900 + 900 + 8500 - 7300
= 26400
Therefore, the amount of stockholders’ equity as of August 31 of the current year is
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